It's really really not about resource allocation, it's about autonomy and choice, and the state's relationship to those things. The thing to appreciate is that the state cannot stand back from this, it is taking a position either way - currently in most countries it actively compels people to live.
The distinction to be drawn between medically-related euthanasia and suicide in other circumstances is basically autonomy and choice. We tend to generally deem suicidal tendencies in healthy people a form of mental illness (particularly for teenagers). This makes it evidence of impaired rationality, and impels the state to try to prevent the potential harm to the individual. The same sorts of paternalistic transfer of decision-making occurs as occurs with such cases as occurs with, say, children - either the state or next of kin gets to make the decisions.
Yet, despite that conceptual argument for stopping non-medical suicides, aside from putting people on death watch, we actually pretty much let people who have psychological burdens kill themselves with impunity. If they're of able body and a degree of shrewdness that means they don't just get locked up and strapped down 'for their own good' then they're pretty much free to kill themselves
I don't think that's really true, though. (At least in the United States; I don't know how they run things in other countries.) They do make serious efforts to stop people from committing suicide if they can -- people have been tackled, tazed, etc, to prevent them from committing suicide. (I seem to recall a case where a man was shot nonfatally to prevent him from shooting himself -- an irony if I ever heard one -- but I don't have a source for that.) As a practical matter there's little the law can do to prevent suicide by able-bodied individuals, but legally speaking, it's not an acceptable activity, and the state can and does use force to prevent it.
Now maybe it's actually wrong that we prevent people who are healthy but want to die from exercising their full autonomy even to the limited extent that we do. I'm certainly open to the argument that suicide is a perfectly rational response to the human condition and what we call mental illness is usually just a different reaction to the futility and pointlessness of existence. Also, it does seem that if you have a right to life you must have a right to waive it (otherwise it's actually an obligation to life). But even then, there's also the collateral damage a suicide inflicts on loved-ones, so perhaps those third party harms are another justification for separating medical euthanasia and suicide from regular suicide (although this would also be an argument for allowing next of kin to override an assisted suicide decision...).
I don't think suicide is inherently irrational or a sign of mental illness. That's commonly argued as a matter of what seems almost like dogma among mental health professionals, but I honestly don't see any particular reason to believe that it's true. So I'd agree with you there.
I'm not sure I agree, though, with your idea that a right must always be able to be waived in order for it to not be an obligation -- a right is always an obligation of some sort. When I say that I have the right to freedom of religion, what we're really saying is that the government cannot (Or really, should not, because it's not a statement of practicality) tell me what to believe in religious matters, which isn't much different from saying that it has an obligation to not control or unduly influence me in that way. Since life is so fundamental, I'm not sure it's incoherent to argue that the right to life is so important that it comes with an obligation to life, as well as an obligation on the part of others to respect it.
But going back to your question, Elrohir, under the status quo I'd argue you've got it backwards, we're actually not "unfairly favouring" physical pain but the reverse. People who are incapable of doing themselves in autonomously, cannot do so, even though they have what we would, as humans, generally consider a far better case for the rationality of suicide than the random suicide by bridge. Legalising assisted suicide and euthanasia would seem to be redressing this imbalance.
I agree that under the current system we effectively, although I don't think intentionally, favor those with mental problems over those with physical, debilitating conditions by effectively giving them more control over whether or not they live. But I'm not making an argument about the status quo, I'm making an argument about a hypothetical system where euthanasia is available for the terminally ill but not for anyone else.
Finally, as further support to the rationality basis for separating medical suciide from the regular kind, I'd submit the example of the doomed dictator or criminal killing themselves to escape capture and punishment. They, like the teenage girl, are perfectly healthy people, yet most of us can see an element of understandability that is simply lacking in a regular depression-related suicide by an ordinary citizen.
And a further personal example. A few years ago at another forum, a regular poster killed herself. She'd been depressed for as long as anyone knew her, and had recently diagnosed as bipolar and schizophrenic. Her life was suffering, she knew she couldn't get better, that she'd never be happy, that the best she could hope for was drugs, medically-induced oblivion of her personality and an inability to feel anything at all. I find it hard to consider her decision to kill herself irrational or unfounded in objective suffering. So you're right that it's not just physcial suffering which can make suicide seem fairly understandable - but as I say, people who are able-bodied are capable of suicide by thier own hand and the state doesn't really do much to stop them.
It's extremely tricky terrain, but the key lens to see things through is what is the state's role, and I'd argue that if there's even a small amount of rationality there, the state already leaves regular suicide alone (despite what the law may say) and should do likewise with the medically-induced kind, it should enable choice instead of obliging people to live.
That's all very interesting, and I just have one small point in response:
It really sounds like you think suicide should be effectively legal for those who are fairly rational, even if they aren't terminally ill. But you don't seem to actually favor making it technically legal -- but why not? By making it illegal, we force people to resort to unseemly and often horrific measures. Even if the state shouldn't be involved, if it's really OK for people to commit suicide (Or at least wrong for the state to prevent it) then that should be clearer so that private actors can make sure it's done in a less painful and traumatizing manner for all involved.
I'm not saying I actually think we should legalize suicide. I just don't see a logical reason to differentiate between those who are terminally ill and those who are not, and neither do I see a reason to implicitly but not explicitly allow suicide for those who are not terminally ill. It's it's not generally bad enough to prevent, then why not make the law itself reflect the actual operation of the state?